Final answer:
To make a 5% boric acid ointment from a 20g of 9% base, the pharmacist needs to add 16 grams of diluent. This is calculated using the equation C1V1 = C2V2, factoring the initial concentration and desired final concentration.
Step-by-step explanation:
The solution to the question involves a calculation from the realm of pharmacy math, specifically focusing on preparing a diluted concentration from a more concentrated one. To manufacture a 5% ointment from the given 20 grams of a 9% boric acid ointment, we need to determine how much diluent to add. This is done using the equation C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the desired concentration, and V2 is the final volume after adding the diluent.
First, solve for V1, which is the mass of the 9% boric acid ointment being used, which in this case is 20 grams. Then set up the equation as follows:
(9%)(20g) = (5%)V2
This simplifies to:
(9/100)(20g) = (5/100)V2
By solving for V2, we find:
V2 = (9/5)(20g)
V2 = (1.8)(20g) = 36 grams
The final volume of the ointment, after adding the diluent, should be 36 grams. To find how much diluent is needed, subtract the original mass of the ointment from the final mass:
Diluent required = V2 - V1
Diluent required = 36g - 20g = 16g
Therefore, the pharmacist needs to add 16 grams of diluent to the 20 grams of 9% boric acid ointment to make a 5% ointment.